Titlebook: Solving Higher-Order Equations; From Logic to Progra Christian Prehofer Book 1998 Birkhäuser Boston 1998 Hardware.Program Analysis.Theorem

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specification and verification of hardware, software, and mathematics. In these applica­ tions, higher-order logic provides the necessary level of abstraction for con­ cise and natural formulations. The main assets of higher-order logic are quan­ tification over functions or predicates and its abst

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Preview,In this chapter, we informally introduce the main concepts and outline the contributions of this work. Precise definitions are presented in later chapters. We proceed from first-order term rewriting and narrowing to higher-order unification and higher-order narrowing.

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Higher-Order Equational Reasoning,This chapter introduces higher-order unification and term rewriting. First, Section 4.1 reviews a set of transformation rules for full higher-order pre-unification. This is followed by an important special case, higher-order patterns, where unification proceeds almost as in the first-order case.

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Variations of Higher-Order Narrowing,This chapter discusses alternative approaches for solving higher-order equations by narrowing. Most of them are inspired by the different notions of first-order narrowing. Compared to lazy narrowing, for all of them new problems arise due to the higher-order case. For an overview of the approaches, we refer again to Figure 2.2.

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978-1-4612-7278-6Birkhäuser Boston 1998

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